This is where one of the most important numbers of modern mathematics comes in - e.
$\displaystyle e=\lim_{x\rightarrow\infty}(1+\frac{1}{x})^x$
And when compounding continuous interest the formula is:
$\displaystyle A=Pe^{rt}$
where A is the new amount, P is the principal amount, e is a constant, r is the growth rate, and t is time.